Question

Work done in forming a liquid drop of radius $R$ is $W_1$ and that of radius $3R$ is $W_2$. The ratio of work done is:

• A. $1:3$
• B. $1:2$
• C. $1:4$
• D. $1:9$

Answer 1

The correct option is D $1:9$

Surface energy (tension) is amount of work done in increasing the area of the surface film through unity.
$W=T\times 4\pi R^2$
$\Rightarrow \frac{W_1}{W_2}=\frac{T\times 4\pi R^2}{T\times 4\pi {\left(3R\right)}^2}$
$=\frac{T\times 4\pi R^2}{T\times 36\pi R^2}=\frac{1}{9}$
$\therefore W_1:W_2=1:9$